But then came Cruz's announcement, and with it speculation over how the issue could impact the 2016 election and whether it even matters.

Political analysts say Cruz may think he's tamping down any controversy by renouncing his Canadian citizenship, but it may come back to haunt him like President Obama's birth certificate did in the 2008 race.

"If we learned anything from the allegations surrounding President Obama's citizenship, it's this: Facts may be stubborn things, but people's beliefs can be a lot more stubborn than the facts," Dante Scala, a political scientist at the University of New Hampshire, told USA Today.

"Many people believe what they want to believe, regardless of the facts, especially when it's about a public figure they do not like in the first place."

The US Constitution allows only a "natural-born" American citizen to serve as president.

But while most legal scholars agree that includes an American born overseas to American parents, the Constitution says nothing about would-be presidents born with dual citizenship, according to the Dallas Morning News.